Vietnam Journal of Mechanics

Dynamic response of the micro-perforated crab beam used in MEMS vibratory gyroscope device

Vu Van The — 2024-02-22

This paper presents a study on the dynamic response of the micro-beams with the crab shape and cut-out holes on the whole operating faces of the beam to create the micro-perforated beam by using FEM simulation software. The obtained results show that the size and shape form of the cut-out holes affect the mechanical responses of the beam on which the holes distribute. The equivalent stiffness of perforated micro-beams decreases significantly with the increasing size of the holes on the beam operating face. And thence the major frequencies of the MEMS vibratory gyroscope system that consist of these micro-beams also decrease. The results of the study are basic for being used for optimizing the structure in subsequent research.

Frequency response function of cracked Timoshenko beam measured by a distributed piezoelectric sensor

Nguyen Tien Khiem — 2024-03-31

In the present report, a novel concept of frequency response function (FRF) is introduced for piezoelectric beam. First, a model of Timoshenko beam bonded with a piezoelectric layer is established and used for deriving the conventional frequency response function acknowledged as mechanical frequency response function (MERF). Then, the output charge produced in the piezoelectric layer is calculated from the MFRF and therefore obtained frequency-dependent function is called electrical frequency response function (EFRF) for the integrated beam. This concept of FRF depends only on exciting position and can be explicitly expressed through crack parameters. So that it provides a novel instrument to modal analysis and structural health monitoring of electro-mechanical systems, especially for crack detection in beams using distributed piezoelectric sensor. The sensitivity of EFRF to crack has been examined and illustrated in numerical examples for cracked Timoshenko beam.

Vibration analysis of Timoshenko microbeams made of functionally graded materials on a Winkler-Pasternak elastic foundation

Tran Van Lien — 2024-03-31

In this work, the free vibration analysis of Timoshenko microbeams made of the Functionally Graded Material (FGM) on the Winkler-Paternak elastic foundation based on the Modified Coupled Stress Theory (MCST) is investigated. Material characteristics of the beam vary throughout the thickness according to the power distribution and are estimated through Mori–Tanaka, Hashin-Shtrikman and Voigt homogenization techniques. The Timoshenko microbeam model considering the length scale parameter is applied. The free vibration differential equations of FGM microbeams are established based on the Finite Element Method (FEM) and Kosmatka’s shape functions. The influences of the size-effect, foundation, material, and geometry parameters on the vibration frequency are then analyzed. It is shown that the study can be applied to other FGMs as well as more complex beam structures.

Dynamic response of sandwich beam with porous core excited by two harmonic loads travelling in opposite directions

Tran Quang Hung — 2024-03-31

This paper presents the time history response of a sandwich beam with a porous core subjected to two moving harmonic loads with opposite directions. In the modelling, the beam is combined of two isotropic face sheets and a porous core with symmetric porosity distribution. The quasi-3D shear deformation beam theory in conjunction with Hamilton's variational principle is utilized to set up the governing equations of motion. The Navier solution is used to obtain the displacement field. The accuracy of the study is validated by comparing with existing results in the literature for specific cases. Effects of the velocity and excitation frequency of the moving loads on the deflection-time history are investigated and discussed. Numerical results reveal that in the case of the double-moving harmonic loads in the antiphase, the resonance phenomenon cannot occur when the excitation frequency approaches the natural frequency of the beam.

Analysis of the springback phenomenon using finite element method

Tan Trung Le Tran — 2024-03-31

The springback phenomenon is a significant concern in manufacturing processes, particularly in metal component forming, as it directly affects dimensional control and the shape of formed parts. Accurate prediction and analysis of springback are crucial for achieving precise dimensional control and ensuring the desired final shape. Therefore, this study focuses on analyzing the springback phenomenon using finite element method. The primary objective is to develop a Matlab program for analyzing three-dimensional springback problems. Throughout the research process, the understanding of the phenomenon has been enhanced. The developed program has been successfully implemented to model and simulate the forming process, considering various aspects of the problem. The results of the solutions have been compared and evaluated, leading to important conclusions. The research also outlines future developments in this field. It is hoped that the results and understanding of this research will contribute to the field of computational mechanics and inspire further research.

Analyzing the nonlinear torsional buckling and post-buckling of ES-FG porous cylindrical shells in thermal environment using FSDT in terms of the displacement components

Pham Van Hoan — 2024-03-31

The main aim of this paper is to investigate the nonlinear buckling and post-buckling of eccentrically stiffened sandwich functionally graded porous (FGP) cylindrical shells surrounded by elastic foundations in thermal environments and under torsional load by analytical approach in terms of the displacement components. The shells are reinforced by eccentric rings and stringers attached to the inside and material properties of face sheets and stiffeners are assumed to be continuously graded in the thickness direction. The sandwich cylindrical shell is composed of FG porous core and two FG layer coating. Based on the first order shear deformation theory (FSDT) with von Kármán geometrical nonlinearity and smeared stiffeners technique, the governing equations are derived. Using Galerkin method, the closed form to find critical torsional load and post-buckling load-deflection curves are obtained. The effects of porosity parameters, the thickness of the porous core, temperature, stiffener, foundation, material and dimensional parameters are analyzed.